Make a sweet mesh dawg. Triangles don't share verts.

CreateWorldMesh.cs

using System;
using UnityEngine;
using System.Collections;

public class CreateWorldMesh : MonoBehaviour
{
    public int dimension;

    public void Start()
    {
        MeshFilter meshFilter = GetComponent<MeshFilter>();
        if (meshFilter == null)
        {
            Debug.LogError("MeshFilter not found!");
            return;
        }

        // create square set of points
        Vector3[] points = new Vector3[(int) Math.Pow(dimension + 1, 2)];
        //Debug.Log("points length" + points.Length);
        // fill set with points
        int j = 0;
        for (int x = 0; x <= dimension; x++)
        {
            for (int z = 0; z <= dimension; z++)
            {
                Debug.Log(j);
                points[j] = new Vector3(x, 0, z);
                j++;
            }
        }

        // clear the mesh
        Mesh mesh = new Mesh();

        // create set of verts
        Vector3[] verts = new Vector3[6 * (int) Math.Pow(dimension, 2)];
        //Debug.Log("verts length" + verts.Length);
        // fill set with verts from points
        int k = 0;
        for (int x = 0; x < dimension; x++)
        {
            for (int z = 0; z < dimension; z++)
            {
                // top triangle of quad
                //Debug.Log(k + " " + (z + ((x * dimension) + x) + 0));
                verts[k] = points[z + ((x * dimension) + x) + 0];
                k++;
                //Debug.Log(k + " " + (z + ((x * dimension) + x) + 1));
                verts[k] = points[z + ((x * dimension) + x) + 1];
                k++;
                //Debug.Log(k + " " + (z + ((x * dimension) + x) + dimension + 2));
                verts[k] = points[z + ((x * dimension) + x) + dimension + 2];
                k++;

                // bottom triangle of quad
                //Debug.Log(k + " " + (z + ((x * dimension) + x) + 0));
                verts[k] = points[z + ((x * dimension) + x) + 0];
                k++;
                //Debug.Log(k + " " + (z + ((x * dimension) + x) + dimension + 2));
                verts[k] = points[z + ((x * dimension) + x) + dimension + 2];
                k++;
                //Debug.Log(k + " " + (z + ((x * dimension) + x) + dimension + 1));
                verts[k] = points[z + ((x * dimension) + x) + dimension + 1];
                k++;
            }
        }

        // create set of triangles
        int[] tris = new int[6 * (int) Math.Pow(dimension, 2)];
        for (int i = 0; i < tris.Length; i++)
        {
            tris[i] = i;
        }

        // assign everything to mesh
        mesh.vertices = verts;
        mesh.triangles = tris;
        mesh.RecalculateNormals();
        mesh.RecalculateBounds();
        mesh.Optimize();
        meshFilter.mesh = mesh;
    }
}